Over the past few decades, transform-based compression technology for image and video sources has gained widespread popularity for visual information management, processing, and communications. As a result, several industry standards have been developed, such as JPEG for still image coding, and MPEG and H.26× for video coding. In general, image and video processing methods compliant with these standards are implemented by dividing an image frame(s) into nonoverlapping blocks, and applying a transformation to each block before applying both quantization and entropy coding. A two-dimensional discrete cosine transform (DCT) is the most common transform used in these methods.
The probability distribution of DCT coefficients is often used in the design and optimization of a quantizer, entropy coder, and related video processing algorithms for use in various signal/image processing equipment (e.g., encoders, decoders, etc.). Determining the probability distribution of DCT coefficients is particularly helpful in rate control for video coding, since the design of a rate control algorithm, and in particular, optimal bit allocation and quantization scale selection, can require knowledge of a rate-distortion relation as a function of the encoder parameters and the video source statistics. The rate-distortion relation can be derived mathematically using the probability distribution of the DCT coefficients. Various distribution models for the AC coefficients have been proposed, including Gaussian distributions and Laplacian distributions.
FIG. 1 shows a schematic diagram of a typical plot of a histogram of discrete cosine transform (DCT) coefficients for an 8×8 block-based DCT of an image, for which the DC coefficients are excluded. The image used here is from a frame of a commonly used anchor video sequence, the AKIYO sequence in QCIF format. The DCT coefficient distribution is most commonly approximated by a Laplacian probability density function (pdf) with parameter λ:
                                          p            ⁡                          (              x              )                                =                                    λ              2                        ⁢            exp            ⁢                          {                                                -                  λ                                ⁢                                                    x                                                              }                                      ,                  x          ∈          R                                    Eq        .                                  ⁢        1            The Laplacian density has an exponential form, leading to the property that the tails of the density decay very quickly.
One problem often encountered in coder design using conventional probability density functions is that the actual distributions of the DCT coefficients in image and video applications can differ significantly from the Gaussian distributions and Laplacian distributions commonly assumed. As a result, rate and distortion models based on either of these distributions may fail to estimate the actual rate-distortion-coding parameter relations accurately and reduce the effectiveness of the coder.